Fish Comparisons Simple Models

Alright, so from all of this what do I know?

Speed Differences: Flow increases speed differences Ablation decreases speed differences Darkness increases speed differences Distance increases speed differences Angles around 90 degrees have a bigger difference in speed

Heading Differences: Fish are more aligned when they are around 90 degrees, slightly less in ablated fish

Synchronization: Darkness increases synchronization

NND: Darkness increases NND Flow decreases NND

Nearest Neighbor Bearing: In darkness fish are more in front or behind In flow fish are more in positioned alongside each other

Sets up the functions that will be used later

rad2deg <- function(rad) {(rad * 180) / (pi)}
deg2rad <- function(deg) {(deg * pi) / (180)}
round_any <- function(x, accuracy, f=round){f(x/ accuracy) * accuracy}
ang_mean <- function(x){rad2deg(atan2(mean(sin(deg2rad(x))),mean(cos(deg2rad(x)))))}

fold_angle_0_360_to_0_180 <- function(x){abs(abs(x-180)-180)}

fold_angle_neg_180_180_to_neg_90_90 <- function(x){ifelse(x > 90,90-abs(90-x),ifelse(x < -90, -90+abs(-90-x), x))}

min_n <- function(x,n){sort(x)[1:n]}
max_n <- function(x,n){sort(x,decreasing = TRUE)[1:n]}

Reads in the data and alters it as needed

comp_data <- read.csv("Fish_Comp_Values.csv")
comp_data <- na.omit(comp_data)

comp_data <- comp_data %>% mutate(Flow = ifelse(Flow == "0", "Still Water", "Flowing Water (2 BL/s)")) %>%
                           mutate(Ablation = ifelse(Ablation == "N", "No Ablation", "Ablated")) %>%
                           mutate(Darkness = ifelse(Darkness == "N", "Light", "Dark")) %>%
                           filter(Distance <= 4) %>%
                           filter(abs(Speed_Diff) <= 6) %>% 
                           #mutate(Speed_Diff = abs(Speed_Diff)) %>%
                           mutate(rad_Heading = deg2rad(Heading_Diff)) %>%
                           mutate(sin_Heading = sin(rad_Heading), cos_Heading = cos(rad_Heading)) %>%
                           #mutate(fold_heading_diff = abs(fold_angle_neg_180_180_to_neg_90_90(Heading_Diff))) %>%
                           mutate(Is_Aligned = ifelse(Heading_Diff < 30, 1, 0)) %>%
                           mutate(Is_Reversed = ifelse(Heading_Diff > 150, 1, 0)) %>%
                           separate(Fish, c("Fish1", "Fish2"),sep="x") %>%
                           mutate(Flow = factor(Flow), Ablation = factor(Ablation), Darkness = factor(Darkness)) %>%
                           mutate(Flow = fct_relevel(Flow, c("Still Water","Flowing Water (2 BL/s)"))) %>%
                           mutate(Ablation = fct_relevel(Ablation, c("No Ablation","Ablated"))) %>%
                           mutate(Darkness = fct_relevel(Darkness, c("Light","Dark"))) %>%
                           mutate(rad_Angle = deg2rad(Angle)) %>%
                           mutate(sin_Angle = sin(rad_Angle), cos_Angle = cos(rad_Angle)) %>%
                           mutate(Flow_Ablation = factor(paste(Flow,Ablation,sep=", "))) %>%
                           mutate(Flow_Darkness = factor(paste(Flow,Darkness,sep=", "))) %>%
                           mutate(Flow_Ablation_Darkness = factor(paste(Flow,Ablation,Darkness,sep=", ")))
                           
                           #mutate(Angle = fold_angle_0_360_to_0_180(Angle))

sum_comp_data <- comp_data %>% mutate(X_Distance = round_any(X_Distance,0.25), 
                                      Y_Distance = round_any(abs(Y_Distance),0.25)) %>%
                               group_by(Flow,Ablation,Darkness,X_Distance,Y_Distance) %>%
                               summarise(Speed_Diff = mean(Speed_Diff),
                                         Heading_Diff = ang_mean(Heading_Diff),
                                         Sync = mean(Sync),
                                         #Fold_Heading_Diff = mean(fold_heading_diff),
                                         Is_Aligned = mean(Is_Aligned),
                                         Is_Reversed = mean(Is_Reversed))

`summarise()` has grouped output by 'Flow', 'Ablation', 'Darkness', 'X_Distance'. You can override using the `.groups` argument.

comp_data_switch_fish <- comp_data %>% mutate(Fish3 = Fish1) %>%
                                       mutate(Fish1 = Fish2) %>%
                                       mutate(Fish2 = Fish3) %>%
                                       select(-c(Fish3))

comp_data_NND <- bind_rows(comp_data, comp_data_switch_fish) %>% group_by(Year,Month,Day,Trial,Fish1,Tailbeat_Num) %>%
                                                                 filter(Distance == min(Distance)) %>%
                                                                 ungroup()

comp_data_near_3 <- bind_rows(comp_data, comp_data_switch_fish) %>% group_by(Year,Month,Day,Trial,Fish1,Tailbeat_Num) %>%
                                                                 slice_min(Distance, n = 3) %>%
                                                                 ungroup() %>%
                                                                 distinct(Distance, .keep_all= TRUE)

#Basic Stats

speed_anova <- aov(Speed_Diff ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_NND)

Anova(speed_anova)

Anova Table (Type II tests)

Response: Speed_Diff
               Sum Sq   Df F value   Pr(>F)   
Flow             2.41    1  3.8841 0.048843 * 
Ablation         0.94    1  1.5189 0.217885   
Darkness         1.51    1  2.4373 0.118591   
Flow:Ablation    1.73    1  2.7848 0.095275 . 
Flow:Darkness    6.13    1  9.8771 0.001691 **
Residuals     1731.81 2792                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

heading_anova <- aov(Heading_Diff ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_NND)

Anova(heading_anova)

Anova Table (Type II tests)

Response: Heading_Diff
                Sum Sq   Df F value Pr(>F)
Flow             16270    1  1.6949 0.1931
Ablation          1799    1  0.1874 0.6651
Darkness          4829    1  0.5030 0.4782
Flow:Ablation     1864    1  0.1941 0.6595
Flow:Darkness     7960    1  0.8292 0.3626
Residuals     26802314 2792               

sync_anova <- aov(Sync ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_NND)

Anova(sync_anova)

Anova Table (Type II tests)

Response: Sync
               Sum Sq   Df F value  Pr(>F)  
Flow            0.170    1  2.6935 0.10087  
Ablation        0.111    1  1.7491 0.18610  
Darkness        0.409    1  6.4561 0.01111 *
Flow:Ablation   0.119    1  1.8786 0.17060  
Flow:Darkness   0.083    1  1.3158 0.25145  
Residuals     176.696 2792                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

dist_anova <- aov(Distance ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_NND)

Anova(dist_anova)

Anova Table (Type II tests)

Response: Distance
               Sum Sq   Df  F value    Pr(>F)    
Flow             4.29    1   9.2920  0.002323 ** 
Ablation         0.01    1   0.0165  0.897889    
Darkness        81.34    1 176.0312 < 2.2e-16 ***
Flow:Ablation    0.26    1   0.5650  0.452325    
Flow:Darkness    4.73    1  10.2324  0.001395 ** 
Residuals     1290.12 2792                       
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

angle_anova <- aov(Angle ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_NND)

Anova(angle_anova)

Anova Table (Type II tests)

Response: Angle
                Sum Sq   Df F value    Pr(>F)    
Flow              4064    1  0.4125 0.5207449    
Ablation           642    1  0.0651 0.7985532    
Darkness        131214    1 13.3174 0.0002678 ***
Flow:Ablation     3812    1  0.3869 0.5339723    
Flow:Darkness    20951    1  2.1265 0.1448873    
Residuals     27508911 2792                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Just nearest Fish Speed Diff

comp_data_near_1 <- bind_rows(comp_data, comp_data_switch_fish) %>% group_by(Year,Month,Day,Trial,Fish1,Tailbeat_Num) %>%
                                                                 slice_max(Distance, n = 1) %>%
                                                                 ungroup() %>%
                                                                 distinct(Distance, .keep_all= TRUE)

speed_anova_nn <- aov(Speed_Diff ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_near_1)

Anova(speed_anova_nn)

Anova Table (Type II tests)

Response: Speed_Diff
               Sum Sq   Df F value Pr(>F)
Flow             0.95    1  1.2883 0.2565
Ablation         0.49    1  0.6671 0.4141
Darkness         1.82    1  2.4620 0.1168
Flow:Ablation    0.75    1  1.0157 0.3137
Flow:Darkness    0.09    1  0.1173 0.7320
Residuals     1564.53 2122               

my_comparisons <- list( c("No Ablation, Light", "No Ablation, Dark"))

ggplot(comp_data_near_1, aes(x = interaction(Ablation,Darkness,sep=", "), y = Speed_Diff, fill = interaction(Ablation,Darkness,sep=", ")))+
  geom_violin(outlier.shape = NA) +
  guides(fill = guide_legend(title = "Condition")) +
  scale_fill_manual(values=c("#EEEEEE", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Available Senses on Nearest Speed Diff") +
  xlab("") +
  ylab("Speed Difference (BL/s)") +
  theme_light() +
  facet_wrap(~ Flow, strip.position = "bottom")+
  #stat_compare_means(aes(label = ..p.signif..), method = "t.test", ref.group = "Flow 0, No Ablation, Light")
  #stat_compare_means(comparisons = my_comparisons, label.y = c(7.5,8.5), label = "p.signif", hide.ns = TRUE) +
  theme(axis.title.x=element_blank(),
        axis.text.x=element_blank(),
        axis.ticks.x=element_blank())

Ignoring unknown parameters: outlier.shape

Trying ggpubr

my_comparisons <- list( c("No Ablation, Light", "No Ablation, Dark") )

ggplot(comp_data_near_3, aes(x = interaction(Ablation,Darkness,sep=", "), y = Distance, fill = interaction(Ablation,Darkness,sep=", ")))+
  geom_boxplot(outlier.shape = NA) +
  guides(fill = guide_legend(title = "Condition")) +
  scale_fill_manual(values=c("#EEEEEE", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Available Senses on Nearest Neighbor Distance (NND)") +
  xlab("") +
  ylab("NND (BL)") +
  theme_light() +
  facet_wrap(~ Flow)+
  #stat_compare_means(aes(label = ..p.signif..), method = "t.test", ref.group = "Flow 0, No Ablation, Light")
  stat_compare_means(comparisons = my_comparisons, label.y = c(4.5), label = "p.signif", hide.ns = TRUE) +
  theme(axis.title.x=element_blank(),
        axis.text.x=element_blank(),
        axis.ticks.x=element_blank())

So we need to make all the possible GLMs for these variables and then compare them in order to see which model does best in order to see what actually has effects

# speed_gam_d <- gam(Speed_Diff ~ s(Distance), data = comp_data_near_3)
# speed_gam_d_f <- gam(Speed_Diff ~ s(Distance,by=Flow), data = comp_data_near_3)
# speed_gam_d_a <- gam(Speed_Diff ~ s(Distance,by=Ablation), data = comp_data_near_3)
# speed_gam_d_d <- gam(Speed_Diff ~ s(Distance,by=Darkness), data = comp_data_near_3)
# speed_gam_d_fa <- gam(Speed_Diff ~ s(Distance,by=Flow_Ablation), data = comp_data_near_3)
# speed_gam_d_fd <- gam(Speed_Diff ~ s(Distance,by=Flow_Darkness), data = comp_data_near_3)
# speed_gam_d_fda <- gam(Speed_Diff ~ s(Distance,by=Flow_Ablation_Darkness), data = comp_data_near_3)
# 
# speed_gam_ca <- gam(Speed_Diff ~ s(cos_Angle), data = comp_data_near_3)
# speed_gam_ca_f <- gam(Speed_Diff ~ s(cos_Angle,by=Flow), data = comp_data_near_3)
# speed_gam_ca_a <- gam(Speed_Diff ~ s(cos_Angle,by=Ablation), data = comp_data_near_3)
# speed_gam_ca_d <- gam(Speed_Diff ~ s(cos_Angle,by=Darkness), data = comp_data_near_3)
# speed_gam_ca_fa <- gam(Speed_Diff ~ s(cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
# speed_gam_ca_fd <- gam(Speed_Diff ~ s(cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
# speed_gam_ca_fda <- gam(Speed_Diff ~ s(cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
# 
# speed_gam_sa <- gam(Speed_Diff ~ s(sin_Angle), data = comp_data_near_3)
# speed_gam_sa_f <- gam(Speed_Diff ~ s(sin_Angle,by=Flow), data = comp_data_near_3)
# speed_gam_sa_a <- gam(Speed_Diff ~ s(sin_Angle,by=Ablation), data = comp_data_near_3)
# speed_gam_sa_d <- gam(Speed_Diff ~ s(sin_Angle,by=Darkness), data = comp_data_near_3)
# speed_gam_sa_fa <- gam(Speed_Diff ~ s(sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
# speed_gam_sa_fd <- gam(Speed_Diff ~ s(sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
# speed_gam_sa_fda <- gam(Speed_Diff ~ s(sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
# 
# speed_gam_dca <- gam(Speed_Diff ~ s(Distance,cos_Angle), data = comp_data_near_3)
# speed_gam_dca_f <- gam(Speed_Diff ~ s(Distance,cos_Angle,by=Flow), data = comp_data_near_3)
# speed_gam_dca_a <- gam(Speed_Diff ~ s(Distance,cos_Angle,by=Ablation), data = comp_data_near_3)
# speed_gam_dca_d <- gam(Speed_Diff ~ s(Distance,cos_Angle,by=Darkness), data = comp_data_near_3)
# speed_gam_dca_fa <- gam(Speed_Diff ~ s(Distance,cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
# speed_gam_dca_fd <- gam(Speed_Diff ~ s(Distance,cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
# speed_gam_dca_fda <- gam(Speed_Diff ~ s(Distance,cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
# 
# speed_gam_dsa <- gam(Speed_Diff ~ s(Distance,sin_Angle), data = comp_data_near_3)
# speed_gam_dsa_f <- gam(Speed_Diff ~ s(Distance,sin_Angle,by=Flow), data = comp_data_near_3)
# speed_gam_dsa_a <- gam(Speed_Diff ~ s(Distance,sin_Angle,by=Ablation), data = comp_data_near_3)
# speed_gam_dsa_d <- gam(Speed_Diff ~ s(Distance,sin_Angle,by=Darkness), data = comp_data_near_3)
# speed_gam_dsa_fa <- gam(Speed_Diff ~ s(Distance,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
# speed_gam_dsa_fd <- gam(Speed_Diff ~ s(Distance,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
# speed_gam_dsa_fda <- gam(Speed_Diff ~ s(Distance,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
# 
# speed_gam_dcasa <- gam(Speed_Diff ~ s(Distance,cos_Angle,sin_Angle), data = comp_data_near_3)
# speed_gam_dcasa_f <- gam(Speed_Diff ~ s(Distance,cos_Angle,sin_Angle,by=Flow), data = comp_data_near_3)
# speed_gam_dcasa_a <- gam(Speed_Diff ~ s(Distance,cos_Angle,sin_Angle,by=Ablation), data = comp_data_near_3)
# speed_gam_dcasa_d <- gam(Speed_Diff ~ s(Distance,cos_Angle,sin_Angle,by=Darkness), data = comp_data_near_3)
# speed_gam_dcasa_fa <- gam(Speed_Diff ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
# speed_gam_dcasa_fd <- gam(Speed_Diff ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
# speed_gam_dcasa_fda <- gam(Speed_Diff ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

speed_AIC <- AIC(speed_gam_d,speed_gam_d_f,speed_gam_d_a,speed_gam_d_d,speed_gam_d_fa,speed_gam_d_fd,speed_gam_d_fda,
                 speed_gam_ca,speed_gam_ca_f,speed_gam_ca_a,speed_gam_ca_d,speed_gam_ca_fa,speed_gam_ca_fd,speed_gam_ca_fda,
                 speed_gam_sa,speed_gam_sa_f,speed_gam_sa_a,speed_gam_sa_d,speed_gam_sa_fa,speed_gam_sa_fd,speed_gam_sa_fda,
                 speed_gam_dca,speed_gam_dca_f,speed_gam_dca_a,speed_gam_dca_d,speed_gam_dca_fa,speed_gam_dca_fd,speed_gam_dca_fda,
                 speed_gam_dsa,speed_gam_dsa_f,speed_gam_dsa_a,speed_gam_dsa_d,speed_gam_dsa_fa,speed_gam_dsa_fd,speed_gam_dsa_fda,
                 speed_gam_dcasa,speed_gam_dcasa_f,speed_gam_dcasa_a,speed_gam_dcasa_d,speed_gam_dcasa_fa,speed_gam_dcasa_fd,speed_gam_dcasa_fda)

Error in AIC(speed_gam_d, speed_gam_d_f, speed_gam_d_a, speed_gam_d_d,  : 
  object 'speed_gam_d' not found

How we do that for the cosine of the headings

cos_heading_gam_d <- gam(cos_Heading ~ s(Distance), data = comp_data_near_3)
cos_heading_gam_d_f <- gam(cos_Heading ~ s(Distance,by=Flow), data = comp_data_near_3)
cos_heading_gam_d_a <- gam(cos_Heading ~ s(Distance,by=Ablation), data = comp_data_near_3)
cos_heading_gam_d_d <- gam(cos_Heading ~ s(Distance,by=Darkness), data = comp_data_near_3)
cos_heading_gam_d_fa <- gam(cos_Heading ~ s(Distance,by=Flow_Ablation), data = comp_data_near_3)
cos_heading_gam_d_fd <- gam(cos_Heading ~ s(Distance,by=Flow_Darkness), data = comp_data_near_3)
cos_heading_gam_d_fda <- gam(cos_Heading ~ s(Distance,by=Flow_Ablation_Darkness), data = comp_data_near_3)

cos_heading_gam_ca <- gam(cos_Heading ~ s(cos_Angle), data = comp_data_near_3)
cos_heading_gam_ca_f <- gam(cos_Heading ~ s(cos_Angle,by=Flow), data = comp_data_near_3)
cos_heading_gam_ca_a <- gam(cos_Heading ~ s(cos_Angle,by=Ablation), data = comp_data_near_3)
cos_heading_gam_ca_d <- gam(cos_Heading ~ s(cos_Angle,by=Darkness), data = comp_data_near_3)
cos_heading_gam_ca_fa <- gam(cos_Heading ~ s(cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
cos_heading_gam_ca_fd <- gam(cos_Heading ~ s(cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
cos_heading_gam_ca_fda <- gam(cos_Heading ~ s(cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

cos_heading_gam_sa <- gam(cos_Heading ~ s(sin_Angle), data = comp_data_near_3)
cos_heading_gam_sa_f <- gam(cos_Heading ~ s(sin_Angle,by=Flow), data = comp_data_near_3)
cos_heading_gam_sa_a <- gam(cos_Heading ~ s(sin_Angle,by=Ablation), data = comp_data_near_3)
cos_heading_gam_sa_d <- gam(cos_Heading ~ s(sin_Angle,by=Darkness), data = comp_data_near_3)
cos_heading_gam_sa_fa <- gam(cos_Heading ~ s(sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
cos_heading_gam_sa_fd <- gam(cos_Heading ~ s(sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
cos_heading_gam_sa_fda <- gam(cos_Heading ~ s(sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

cos_heading_gam_dca <- gam(cos_Heading ~ s(Distance,cos_Angle), data = comp_data_near_3)
cos_heading_gam_dca_f <- gam(cos_Heading ~ s(Distance,cos_Angle,by=Flow), data = comp_data_near_3)
cos_heading_gam_dca_a <- gam(cos_Heading ~ s(Distance,cos_Angle,by=Ablation), data = comp_data_near_3)
cos_heading_gam_dca_d <- gam(cos_Heading ~ s(Distance,cos_Angle,by=Darkness), data = comp_data_near_3)
cos_heading_gam_dca_fa <- gam(cos_Heading ~ s(Distance,cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
cos_heading_gam_dca_fd <- gam(cos_Heading ~ s(Distance,cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
cos_heading_gam_dca_fda <- gam(cos_Heading ~ s(Distance,cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

cos_heading_gam_dsa <- gam(cos_Heading ~ s(Distance,sin_Angle), data = comp_data_near_3)
cos_heading_gam_dsa_f <- gam(cos_Heading ~ s(Distance,sin_Angle,by=Flow), data = comp_data_near_3)
cos_heading_gam_dsa_a <- gam(cos_Heading ~ s(Distance,sin_Angle,by=Ablation), data = comp_data_near_3)
cos_heading_gam_dsa_d <- gam(cos_Heading ~ s(Distance,sin_Angle,by=Darkness), data = comp_data_near_3)
cos_heading_gam_dsa_fa <- gam(cos_Heading ~ s(Distance,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
cos_heading_gam_dsa_fd <- gam(cos_Heading ~ s(Distance,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
cos_heading_gam_dsa_fda <- gam(cos_Heading ~ s(Distance,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

cos_heading_gam_dcasa <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle), data = comp_data_near_3)
cos_heading_gam_dcasa_f <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow), data = comp_data_near_3)
cos_heading_gam_dcasa_a <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Ablation), data = comp_data_near_3)
cos_heading_gam_dcasa_d <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Darkness), data = comp_data_near_3)
cos_heading_gam_dcasa_fa <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
cos_heading_gam_dcasa_fd <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
cos_heading_gam_dcasa_fda <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

cos_heading_AIC <- AIC(cos_heading_gam_d,cos_heading_gam_d_f,cos_heading_gam_d_a,cos_heading_gam_d_d,cos_heading_gam_d_fa,cos_heading_gam_d_fd,cos_heading_gam_d_fda,
                 cos_heading_gam_ca,cos_heading_gam_ca_f,cos_heading_gam_ca_a,cos_heading_gam_ca_d,cos_heading_gam_ca_fa,cos_heading_gam_ca_fd,cos_heading_gam_ca_fda,
                 cos_heading_gam_sa,cos_heading_gam_sa_f,cos_heading_gam_sa_a,cos_heading_gam_sa_d,cos_heading_gam_sa_fa,cos_heading_gam_sa_fd,cos_heading_gam_sa_fda,
                 cos_heading_gam_dca,cos_heading_gam_dca_f,cos_heading_gam_dca_a,cos_heading_gam_dca_d,cos_heading_gam_dca_fa,cos_heading_gam_dca_fd,cos_heading_gam_dca_fda,
                 cos_heading_gam_dsa,cos_heading_gam_dsa_f,cos_heading_gam_dsa_a,cos_heading_gam_dsa_d,cos_heading_gam_dsa_fa,cos_heading_gam_dsa_fd,cos_heading_gam_dsa_fda,
                 cos_heading_gam_dcasa,cos_heading_gam_dcasa_f,cos_heading_gam_dcasa_a,cos_heading_gam_dcasa_d,cos_heading_gam_dcasa_fa,cos_heading_gam_dcasa_fd,cos_heading_gam_dcasa_fda)


cos_heading_AIC <- tibble::rownames_to_column(cos_heading_AIC, "Model_Name")

cos_heading_AIC <- cos_heading_AIC %>% mutate(Model_Name = fct_reorder(Model_Name, -AIC)) %>% arrange(AIC)

ggplot(cos_heading_AIC %>% arrange(AIC), aes(x = Model_Name, y = AIC)) +
  geom_point(color = "blue") +
  xlab("") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  theme_light() +
  scale_y_reverse() +
  coord_flip()

cos_heading_AIC

Now with the sin of the Headings

sin_heading_gam_d <- gam(sin_Heading ~ s(Distance), data = comp_data_near_3)
sin_heading_gam_d_f <- gam(sin_Heading ~ s(Distance,by=Flow), data = comp_data_near_3)
sin_heading_gam_d_a <- gam(sin_Heading ~ s(Distance,by=Ablation), data = comp_data_near_3)
sin_heading_gam_d_d <- gam(sin_Heading ~ s(Distance,by=Darkness), data = comp_data_near_3)
sin_heading_gam_d_fa <- gam(sin_Heading ~ s(Distance,by=Flow_Ablation), data = comp_data_near_3)
sin_heading_gam_d_fd <- gam(sin_Heading ~ s(Distance,by=Flow_Darkness), data = comp_data_near_3)
sin_heading_gam_d_fda <- gam(sin_Heading ~ s(Distance,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sin_heading_gam_ca <- gam(sin_Heading ~ s(cos_Angle), data = comp_data_near_3)
sin_heading_gam_ca_f <- gam(sin_Heading ~ s(cos_Angle,by=Flow), data = comp_data_near_3)
sin_heading_gam_ca_a <- gam(sin_Heading ~ s(cos_Angle,by=Ablation), data = comp_data_near_3)
sin_heading_gam_ca_d <- gam(sin_Heading ~ s(cos_Angle,by=Darkness), data = comp_data_near_3)
sin_heading_gam_ca_fa <- gam(sin_Heading ~ s(cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
sin_heading_gam_ca_fd <- gam(sin_Heading ~ s(cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
sin_heading_gam_ca_fda <- gam(sin_Heading ~ s(cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sin_heading_gam_sa <- gam(sin_Heading ~ s(sin_Angle), data = comp_data_near_3)
sin_heading_gam_sa_f <- gam(sin_Heading ~ s(sin_Angle,by=Flow), data = comp_data_near_3)
sin_heading_gam_sa_a <- gam(sin_Heading ~ s(sin_Angle,by=Ablation), data = comp_data_near_3)
sin_heading_gam_sa_d <- gam(sin_Heading ~ s(sin_Angle,by=Darkness), data = comp_data_near_3)
sin_heading_gam_sa_fa <- gam(sin_Heading ~ s(sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
sin_heading_gam_sa_fd <- gam(sin_Heading ~ s(sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
sin_heading_gam_sa_fda <- gam(sin_Heading ~ s(sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sin_heading_gam_dca <- gam(sin_Heading ~ s(Distance,cos_Angle), data = comp_data_near_3)
sin_heading_gam_dca_f <- gam(sin_Heading ~ s(Distance,cos_Angle,by=Flow), data = comp_data_near_3)
sin_heading_gam_dca_a <- gam(sin_Heading ~ s(Distance,cos_Angle,by=Ablation), data = comp_data_near_3)
sin_heading_gam_dca_d <- gam(sin_Heading ~ s(Distance,cos_Angle,by=Darkness), data = comp_data_near_3)
sin_heading_gam_dca_fa <- gam(sin_Heading ~ s(Distance,cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
sin_heading_gam_dca_fd <- gam(sin_Heading ~ s(Distance,cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
sin_heading_gam_dca_fda <- gam(sin_Heading ~ s(Distance,cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sin_heading_gam_dsa <- gam(sin_Heading ~ s(Distance,sin_Angle), data = comp_data_near_3)
sin_heading_gam_dsa_f <- gam(sin_Heading ~ s(Distance,sin_Angle,by=Flow), data = comp_data_near_3)
sin_heading_gam_dsa_a <- gam(sin_Heading ~ s(Distance,sin_Angle,by=Ablation), data = comp_data_near_3)
sin_heading_gam_dsa_d <- gam(sin_Heading ~ s(Distance,sin_Angle,by=Darkness), data = comp_data_near_3)
sin_heading_gam_dsa_fa <- gam(sin_Heading ~ s(Distance,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
sin_heading_gam_dsa_fd <- gam(sin_Heading ~ s(Distance,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
sin_heading_gam_dsa_fda <- gam(sin_Heading ~ s(Distance,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sin_heading_gam_dcasa <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle), data = comp_data_near_3)
sin_heading_gam_dcasa_f <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow), data = comp_data_near_3)
sin_heading_gam_dcasa_a <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Ablation), data = comp_data_near_3)
sin_heading_gam_dcasa_d <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Darkness), data = comp_data_near_3)
sin_heading_gam_dcasa_fa <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
sin_heading_gam_dcasa_fd <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
sin_heading_gam_dcasa_fda <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sin_Heading_AIC <- AIC(sin_heading_gam_d,sin_heading_gam_d_f,sin_heading_gam_d_a,sin_heading_gam_d_d,sin_heading_gam_d_fa,sin_heading_gam_d_fd,sin_heading_gam_d_fda,
                 sin_heading_gam_ca,sin_heading_gam_ca_f,sin_heading_gam_ca_a,sin_heading_gam_ca_d,sin_heading_gam_ca_fa,sin_heading_gam_ca_fd,sin_heading_gam_ca_fda,
                 sin_heading_gam_sa,sin_heading_gam_sa_f,sin_heading_gam_sa_a,sin_heading_gam_sa_d,sin_heading_gam_sa_fa,sin_heading_gam_sa_fd,sin_heading_gam_sa_fda,
                 sin_heading_gam_dca,sin_heading_gam_dca_f,sin_heading_gam_dca_a,sin_heading_gam_dca_d,sin_heading_gam_dca_fa,sin_heading_gam_dca_fd,sin_heading_gam_dca_fda,
                 sin_heading_gam_dsa,sin_heading_gam_dsa_f,sin_heading_gam_dsa_a,sin_heading_gam_dsa_d,sin_heading_gam_dsa_fa,sin_heading_gam_dsa_fd,sin_heading_gam_dsa_fda,
                 sin_heading_gam_dcasa,sin_heading_gam_dcasa_f,sin_heading_gam_dcasa_a,sin_heading_gam_dcasa_d,sin_heading_gam_dcasa_fa,sin_heading_gam_dcasa_fd,sin_heading_gam_dcasa_fda)


sin_Heading_AIC <- tibble::rownames_to_column(sin_Heading_AIC, "Model_Name")

sin_Heading_AIC <- sin_Heading_AIC %>% mutate(Model_Name = fct_reorder(Model_Name, -AIC)) %>% arrange(AIC)

ggplot(sin_Heading_AIC %>% arrange(AIC), aes(x = Model_Name, y = AIC)) +
  geom_point(color = "blue") +
  xlab("") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  theme_light()+
  scale_y_reverse() +
  coord_flip()

sin_Heading_AIC

And now with Sync

sync_gam_d <- gam(Sync ~ s(Distance), data = comp_data_near_3)
sync_gam_d_f <- gam(Sync ~ s(Distance,by=Flow), data = comp_data_near_3)
sync_gam_d_a <- gam(Sync ~ s(Distance,by=Ablation), data = comp_data_near_3)
sync_gam_d_d <- gam(Sync ~ s(Distance,by=Darkness), data = comp_data_near_3)
sync_gam_d_fa <- gam(Sync ~ s(Distance,by=Flow_Ablation), data = comp_data_near_3)
sync_gam_d_fd <- gam(Sync ~ s(Distance,by=Flow_Darkness), data = comp_data_near_3)
sync_gam_d_fda <- gam(Sync ~ s(Distance,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sync_gam_ca <- gam(Sync ~ s(cos_Angle), data = comp_data_near_3)
sync_gam_ca_f <- gam(Sync ~ s(cos_Angle,by=Flow), data = comp_data_near_3)
sync_gam_ca_a <- gam(Sync ~ s(cos_Angle,by=Ablation), data = comp_data_near_3)
sync_gam_ca_d <- gam(Sync ~ s(cos_Angle,by=Darkness), data = comp_data_near_3)
sync_gam_ca_fa <- gam(Sync ~ s(cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
sync_gam_ca_fd <- gam(Sync ~ s(cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
sync_gam_ca_fda <- gam(Sync ~ s(cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sync_gam_sa <- gam(Sync ~ s(sin_Angle), data = comp_data_near_3)
sync_gam_sa_f <- gam(Sync ~ s(sin_Angle,by=Flow), data = comp_data_near_3)
sync_gam_sa_a <- gam(Sync ~ s(sin_Angle,by=Ablation), data = comp_data_near_3)
sync_gam_sa_d <- gam(Sync ~ s(sin_Angle,by=Darkness), data = comp_data_near_3)
sync_gam_sa_fa <- gam(Sync ~ s(sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
sync_gam_sa_fd <- gam(Sync ~ s(sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
sync_gam_sa_fda <- gam(Sync ~ s(sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sync_gam_dca <- gam(Sync ~ s(Distance,cos_Angle), data = comp_data_near_3)
sync_gam_dca_f <- gam(Sync ~ s(Distance,cos_Angle,by=Flow), data = comp_data_near_3)
sync_gam_dca_a <- gam(Sync ~ s(Distance,cos_Angle,by=Ablation), data = comp_data_near_3)
sync_gam_dca_d <- gam(Sync ~ s(Distance,cos_Angle,by=Darkness), data = comp_data_near_3)
sync_gam_dca_fa <- gam(Sync ~ s(Distance,cos_Angle,by=Flow_Ablation), data = comp_data_near_3)
sync_gam_dca_fd <- gam(Sync ~ s(Distance,cos_Angle,by=Flow_Darkness), data = comp_data_near_3)
sync_gam_dca_fda <- gam(Sync ~ s(Distance,cos_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sync_gam_dsa <- gam(Sync ~ s(Distance,sin_Angle), data = comp_data_near_3)
sync_gam_dsa_f <- gam(Sync ~ s(Distance,sin_Angle,by=Flow), data = comp_data_near_3)
sync_gam_dsa_a <- gam(Sync ~ s(Distance,sin_Angle,by=Ablation), data = comp_data_near_3)
sync_gam_dsa_d <- gam(Sync ~ s(Distance,sin_Angle,by=Darkness), data = comp_data_near_3)
sync_gam_dsa_fa <- gam(Sync ~ s(Distance,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
sync_gam_dsa_fd <- gam(Sync ~ s(Distance,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
sync_gam_dsa_fda <- gam(Sync ~ s(Distance,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

sync_gam_dcasa <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle), data = comp_data_near_3)
sync_gam_dcasa_f <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle,by=Flow), data = comp_data_near_3)
sync_gam_dcasa_a <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle,by=Ablation), data = comp_data_near_3)
sync_gam_dcasa_d <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle,by=Darkness), data = comp_data_near_3)
sync_gam_dcasa_fa <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation), data = comp_data_near_3)
sync_gam_dcasa_fd <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Darkness), data = comp_data_near_3)
sync_gam_dcasa_fda <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)

Sync_AIC <- AIC(sync_gam_d,sync_gam_d_f,sync_gam_d_a,sync_gam_d_d,sync_gam_d_fa,sync_gam_d_fd,sync_gam_d_fda,
                 sync_gam_ca,sync_gam_ca_f,sync_gam_ca_a,sync_gam_ca_d,sync_gam_ca_fa,sync_gam_ca_fd,sync_gam_ca_fda,
                 sync_gam_sa,sync_gam_sa_f,sync_gam_sa_a,sync_gam_sa_d,sync_gam_sa_fa,sync_gam_sa_fd,sync_gam_sa_fda,
                 sync_gam_dca,sync_gam_dca_f,sync_gam_dca_a,sync_gam_dca_d,sync_gam_dca_fa,sync_gam_dca_fd,sync_gam_dca_fda,
                 sync_gam_dsa,sync_gam_dsa_f,sync_gam_dsa_a,sync_gam_dsa_d,sync_gam_dsa_fa,sync_gam_dsa_fd,sync_gam_dsa_fda,
                 sync_gam_dcasa,sync_gam_dcasa_f,sync_gam_dcasa_a,sync_gam_dcasa_d,sync_gam_dcasa_fa,sync_gam_dcasa_fd,sync_gam_dcasa_fda)


Sync_AIC <- tibble::rownames_to_column(Sync_AIC, "Model_Name")

Sync_AIC <- Sync_AIC %>% mutate(Model_Name = fct_reorder(Model_Name, -AIC)) %>% arrange(AIC)

ggplot(Sync_AIC %>% arrange(AIC), aes(x = Model_Name, y = AIC)) +
  geom_point(color = "blue") +
  xlab("") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  theme_light()+
  scale_y_reverse() +
  coord_flip()

Sync_AIC

Now we use the best of those

speed_gam <- speed_gam_dsa_fda <- gam(Speed_Diff ~ s(Distance,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
summary(speed_gam)

Family: gaussian 
Link function: identity 

Formula:
Speed_Diff ~ s(Distance, sin_Angle, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.615882   0.008085   76.17   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                                          edf Ref.df     F  p-value    
s(Distance,sin_Angle):Flow_Ablation_DarknessFlow 0, Ablated, Light      7.487 10.485 4.983 9.89e-07 ***
s(Distance,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Dark   2.618  3.172 3.075  0.02466 *  
s(Distance,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Light  7.496 10.506 2.152  0.01620 *  
s(Distance,sin_Angle):Flow_Ablation_DarknessFlow 2, Ablated, Light     21.323 25.538 2.239  0.00033 ***
s(Distance,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  21.574 25.830 2.912 1.42e-06 ***
s(Distance,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Light 13.769 18.268 1.839  0.01537 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.048   Deviance explained = 6.37%
GCV =   0.26  Scale est. = 0.25566   n = 4511

vis.gam(speed_gam)

data length [31] is not a sub-multiple or multiple of the number of rows [30]

# speed_gam_viz <- getViz(speed_gam)
# plotRGL(sm(speed_gam_viz, 1))

cos_heading_gam <- gam(cos_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
summary(cos_heading_gam)

Family: gaussian 
Link function: identity 

Formula:
cos_Heading ~ s(Distance, cos_Angle, sin_Angle, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.08186    0.01208   6.775 1.41e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                                                    edf Ref.df     F  p-value    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, Ablated, Light     38.161 50.349 1.806 0.000422 ***
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  18.362 24.241 1.183 0.243122    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Light 21.843 29.136 2.469 2.12e-05 ***
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, Ablated, Light     16.910 22.350 1.188 0.240902    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Dark   8.546  9.066 1.534 0.128462    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Light 15.001 19.454 1.419 0.101282    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Rank: 649/655
R-sq.(adj) =  0.0466   Deviance explained = 7.17%
GCV = 0.56674  Scale est. = 0.55169   n = 4511

vis.gam(cos_heading_gam)

data length [31] is not a sub-multiple or multiple of the number of rows [30]

# cos_heading_gam_viz <- getViz(cos_heading_gam)
# plotRGL(sm(cos_heading_gam_viz, 1), fix = c("Distance" = 0))

sin_heading_gam <- gam(sin_Heading ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
summary(sin_heading_gam)

Family: gaussian 
Link function: identity 

Formula:
sin_Heading ~ s(Distance, cos_Angle, sin_Angle, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.00113    0.01019  -0.111    0.912

Approximate significance of smooth terms:
                                                                                   edf Ref.df     F  p-value    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, Ablated, Light     10.51  12.60 2.860 0.000499 ***
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  14.00  18.02 1.546 0.066136 .  
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Light  8.00   8.00 2.767 0.004736 ** 
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, Ablated, Light     15.70  20.64 1.548 0.054157 .  
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  16.94  22.29 1.079 0.367428    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Light  8.00   8.00 1.631 0.110529    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Rank: 646/655
R-sq.(adj) =  0.0247   Deviance explained = 4.05%
GCV = 0.41083  Scale est. = 0.40408   n = 4511

vis.gam(sin_heading_gam)

data length [31] is not a sub-multiple or multiple of the number of rows [30]

# sin_heading_gam_viz <- getViz(sin_heading_gam)
# plotRGL(sm(sin_heading_gam_viz, 1), fix = c("Distance" = 0))

sync_gam <- gam(Sync ~ s(Distance,cos_Angle,sin_Angle,by=Flow_Ablation_Darkness), data = comp_data_near_3)
summary(sync_gam)

Family: gaussian 
Link function: identity 

Formula:
Sync ~ s(Distance, cos_Angle, sin_Angle, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.541844   0.003992   135.7   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                                                   edf Ref.df     F  p-value    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, Ablated, Light     49.42  63.98 1.823 7.94e-05 ***
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  15.35  19.99 1.689  0.02782 *  
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Light 43.25  56.84 1.008  0.45888    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, Ablated, Light     18.36  24.37 1.176  0.23445    
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  20.13  26.71 1.700  0.01386 *  
s(Distance,cos_Angle,sin_Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Light 18.25  24.02 1.832  0.00788 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Rank: 649/655
R-sq.(adj) =  0.0577   Deviance explained = 9.22%
GCV = 0.060991  Scale est. = 0.05875   n = 4511

vis.gam(sync_gam)

data length [31] is not a sub-multiple or multiple of the number of rows [30]

# sync_gam_viz <- getViz(sync_gam)
# plotRGL(sm(sync_gam_viz, 1), fix = c("Distance" = 0))

Now we make some predictions for this.

d <- seq(from = 0, to = 3, by = 0.1)
a <- seq(from = 0, to = 180, by = 5)

flows <- c("Flow 0", "Flow 2")
ablation <- c("No Ablation", "Ablated")
dark <- c("Light","Dark")

predict_df <- expand.grid(Distance = d, Angle = a, Flow = flows, Ablation = ablation, Darkness = dark)

predict_df <- predict_df %>% mutate(Flow_Ablation_Darkness = factor(paste(Flow,Ablation,Darkness,sep=", "))) %>% 
                             filter(!(Ablation == "Ablated" & Darkness == 'Dark')) %>%
                             mutate(rad_Angle = deg2rad(Angle)) %>%
                             mutate(sin_Angle = sin(rad_Angle), cos_Angle = cos(rad_Angle))

predict_df <- predict_df %>% mutate(pred_speed_diff = predict.gam(speed_gam,predict_df),
                                    pred_cos_heading_diff = predict.gam(cos_heading_gam,predict_df),
                                    pred_sin_heading_diff = predict.gam(sin_heading_gam,predict_df),
                                    pred_sync = predict.gam(sync_gam,predict_df)) %>%
                                    mutate(Angle = rad2deg(atan2(sin_Angle,cos_Angle))) %>%
                                    mutate(pred_heading_diff = rad2deg(atan2(pred_sin_heading_diff,pred_cos_heading_diff)))

predict_df_sum <- predict_df %>% group_by(Distance,Flow,Ablation,Darkness) %>%
                             mutate(mean_Speed_Distance = mean(pred_speed_diff), sd_Speed_Distance = sd(pred_speed_diff),
                                    mean_Heading_Distance = mean(pred_heading_diff), sd_Heading_Distance = sd(pred_heading_diff),
                                    mean_Sync_Distance = mean(pred_sync), sd_Sync_Distance = sd(pred_sync)) %>%
                             ungroup() %>%
                             group_by(Angle,Flow,Ablation,Darkness) %>%
                             mutate(mean_Speed_Angle = mean(pred_speed_diff), sd_Speed_Angle = sd(pred_speed_diff),
                                    mean_Heading_Angle = rad2deg(atan(mean(pred_sin_heading_diff)/mean(pred_cos_heading_diff))),
                                    sd_Heading_Angle = rad2deg(atan(sd(pred_sin_heading_diff)/sd(pred_cos_heading_diff))),
                                    mean_Sync_Angle = mean(pred_sync), sd_Sync_Angle = sd(pred_sync)) %>%
                             ungroup()
predict_df_sum <- predict_df %>% group_by(Distance,Flow,Ablation,Darkness) %>%
                             mutate(mean_Speed_Distance = mean(pred_speed_diff), sd_Speed_Distance = sd(pred_speed_diff),
                                    mean_Heading_Distance = mean(pred_heading_diff), sd_Heading_Distance = sd(pred_heading_diff),
                                    mean_Sync_Distance = mean(pred_sync), sd_Sync_Distance = sd(pred_sync)) %>%
                             ungroup() %>%
                             group_by(Angle,Flow,Ablation,Darkness) %>%
                             mutate(mean_Speed_Angle = mean(pred_speed_diff), sd_Speed_Angle = sd(pred_speed_diff),
                                    mean_Heading_Angle = rad2deg(atan(mean(pred_sin_heading_diff)/mean(pred_cos_heading_diff))),
                                    sd_Heading_Angle = rad2deg(atan(sd(pred_sin_heading_diff)/sd(pred_cos_heading_diff))),
                                    mean_Sync_Angle = mean(pred_sync), sd_Sync_Angle = sd(pred_sync)) %>%
                             ungroup()

And now we graph those?

ggplot(predict_df_sum, aes(x = Distance, y = mean_Speed_Distance, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=" "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Distance, y = pred_speed_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Speed_Distance-sd_Speed_Distance, ymax = mean_Speed_Distance+sd_Speed_Distance),
             linetype = 0,
             alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Distance and Senses on Speed Difference") +
  xlab("Distance (BL)") +
  ylab("Speed Difference (BL/s)") +
  #ylim(0,1.5) +
  theme_light()

ggplot(predict_df_sum, aes(x = Distance, y = mean_Heading_Distance, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Distance, y = pred_heading_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Heading_Distance-sd_Heading_Distance, ymax = mean_Heading_Distance+sd_Heading_Distance),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Distance and Senses on Heading Difference") +
  xlab("Distance (BL)") +
  ylab("Heading Difference (Degrees)") +
  #ylim(0,50) +
  theme_light()

ggplot(predict_df_sum, aes(x = Distance, y = mean_Sync_Distance, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Distance, y = pred_sync, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Sync_Distance-sd_Sync_Distance, ymax = mean_Sync_Distance+sd_Sync_Distance),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Distance and Senses on Synchonization") +
  xlab("Distance (BL)") +
  ylab("Synchonization") +
  #ylim(0,1)+
  theme_light()

ggplot(predict_df_sum, aes(x = Angle, y = mean_Speed_Angle, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Angle, y = pred_speed_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Speed_Angle-sd_Speed_Angle, ymax = mean_Speed_Angle+sd_Speed_Angle),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Bearing and Senses on Speed Difference") +
  xlab("Bearing (Degrees)") +
  ylab("Speed Difference (BL/s)") +
  theme_light()

ggplot(predict_df_sum, aes(x = Angle, y = mean_Heading_Angle, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Angle, y = pred_heading_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Heading_Angle-sd_Heading_Angle, ymax = mean_Heading_Angle+sd_Heading_Angle),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Bearing and Senses on Heading Difference") +
  xlab("Angle (Degrees)") +
  ylab("Heading Difference (Degrees)") +
  theme_light()

ggplot(predict_df_sum, aes(x = Angle, y = mean_Sync_Angle, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
 #geom_point(data=predict_df, aes(x = Angle, y = pred_sync, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Sync_Angle-sd_Sync_Angle, ymax = mean_Sync_Angle+sd_Sync_Angle),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Bearing and Senses on Synchonization") +
  xlab("Bearing (Degrees)") +
  ylab("Synchonization") +
  theme_light()

Density vs Things

dist_bin_size <- 1
angle_bin_size <- 30

comp_data_freqs <- comp_data_near_3 %>% mutate(Dist_bin = round_any(Distance, dist_bin_size), 
                                               Angle_bin = round_any(Angle, angle_bin_size)) %>%
                                        group_by(Flow,Darkness,Ablation, Dist_bin, Angle_bin,Flow_Ablation_Darkness) %>%
                                        mutate(Count = n()) %>%
                                        ungroup() %>%
                                        group_by(Flow,Darkness,Ablation,Flow_Ablation_Darkness) %>%
                                        mutate(Freq = Count/n()) %>%
                                        ungroup() %>%
                                        group_by(Flow,Darkness,Ablation,Dist_bin,Angle_bin,Flow_Ablation_Darkness) %>%
                                        summarise(Speed_Diff = mean(Speed_Diff),
                                                  Fold_Heading_Diff = ang_mean(fold_heading_diff),
                                                  Sync = mean(Sync),
                                                  Freq = mean(Freq))

freq_speed_glm <- glm(Speed_Diff ~ Freq*(Flow+Darkness+Ablation+Flow:Ablation+Flow:Darkness), data = comp_data_freqs)

summary(freq_speed_glm)

freq_heading_glm <- glm(Fold_Heading_Diff ~ Freq*(Flow+Darkness+Ablation+Flow:Ablation+Flow:Darkness), data = comp_data_freqs)

summary(freq_heading_glm)

freq_sync_glm <- glm(Sync ~ Freq*(Flow+Darkness+Ablation+Flow:Ablation+Flow:Darkness), data = comp_data_freqs)

summary(freq_sync_glm)

freq_speed_gam <- gam(Speed_Diff ~ s(Freq,by=Flow_Ablation_Darkness),
                              data = comp_data_freqs)

summary(freq_speed_gam)

freq_heading_gam <- gam(Fold_Heading_Diff ~ s(Freq,by=Flow_Ablation_Darkness),
                              data = comp_data_freqs)

summary(freq_heading_gam)

freq_sync_gam <- gam(Sync ~ s(Freq,by=Flow_Ablation_Darkness),
                              data = comp_data_freqs)

summary(freq_sync_gam)

Now we make some predictions for this.

f <- seq(from = 0.005, to = 0.07, by = 0.001)

flows <- c("Flow 0", "Flow 2")
ablation <- c("No Ablation", "Ablated")
dark <- c("Light","Dark")

freq_predict_df <- expand.grid(Freq = f, Flow = flows, Ablation = ablation, Darkness = dark)

freq_predict_df <- freq_predict_df %>% mutate(Flow_Ablation_Darkness = factor(paste(Flow,Ablation,Darkness,sep=", "))) %>% 
                            filter(!(Ablation == "Ablated" & Darkness == 'Dark'))

freq_predict_df <- freq_predict_df %>% mutate(pred_speed_diff = predict.gam(freq_speed_gam,freq_predict_df),
                                    pred_heading_diff = predict.gam(freq_heading_gam,freq_predict_df),
                                    pred_sync = predict.gam(freq_sync_gam,freq_predict_df))

ggplot(comp_data_freqs, aes(x = Freq, y = Speed_Diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", formula = "y ~ x", se = FALSE) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Preference and Senses on Speed Difference") +
  xlab("Frequency of Observations") +
  ylab("Speed Difference (BL/s)") +
  theme_light()

ggplot(comp_data_freqs, aes(x = Freq, y = Fold_Heading_Diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", formula = "y ~ x", se = FALSE) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Preference and Senses on Heading Difference") +
  xlab("Frequency of Observations") +
  ylab("Heading Difference (Degrees)") +
  theme_light()

ggplot(comp_data_freqs, aes(x = Freq, y = Sync, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", formula = "y ~ x", se = FALSE) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Preference and Senses on Synchonization") +
  xlab("Frequency of Observations") +
  ylab("Synchonization") +
  theme_light()

ggplot(freq_predict_df, aes(x = Freq, y = pred_speed_diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Frequency of Observations on Speed Difference") +
  xlab("Frequency (%)") +
  ylab("Speed Difference (BL/s)") +
  theme_light()

ggplot(freq_predict_df, aes(x = Freq, y = pred_heading_diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Frequency of Observations on Heading Difference") +
  xlab("Frequency (%)") +
  ylab("Heading Difference (Degrees)") +
  theme_light()

ggplot(freq_predict_df, aes(x = Freq, y = pred_sync, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Frequency of Observations on Synchonization") +
  xlab("Frequency (%)") +
  ylab("Synchonization") +
  theme_light()